Data Processing and Reliability Analysis

With the parameters listed in Table 1, the expected lifetime for wire bond and solder joint is calculated through Equation (21) and (22). Since the temperature amplitude is preset as ranged from 20°C to 100°C, the mean temperature amplitude, ∆𝑇_𝑚= ²⁰⁺¹⁰⁰₂ = 60℃. Therefore, the expected component lifetime for solder joint and wire bond is computed respectively as:

𝑁_𝑓𝑠 = 0.5 × (0.0004×(21.5−3.2)×80 1.1×0.0004 )

1

−0.49 = 338.78 𝐾 𝑐𝑦𝑐𝑙𝑒𝑠 (44)

𝑁_𝑓𝑤 = 640 × 80⁻⁵× 𝑒𝑥𝑝 (8.314×(273+60)^7.8×104 ) = 355.98 𝐾 𝑐𝑦𝑐𝑙𝑒𝑠 (45) The cycle that causes 3% increase in VGE is treated as NSIth cycle in which the solder joint shows the sign of fatigue. In other words, the crack starts to initiate and propagate in solder joint caused by high junction temperature. Using this criterion and Equation (40), NSIth cycle is calculated as:

𝑁_𝑆𝐼 =^ln

(1+3%)×3129.7 3129.7

4×10⁻⁵ = 54.745 𝐾 (46) Based upon the calculation above, 54.745Kth cycle is the cycle that the solder joint is considered to start fatiguing and taken into account for system reliability prediction. Hence, from this point on, junction temperature is effect by not only the degradation process of wire bond, but also solder joint. According to this finding, the increase junction temperature is calculated as the following equation depending to the specific cycle

745

Using the parameters from Table 3 via Equations (31) and (32) defined in proposal model, the change in junction temperature due to component degradation is computed as a function of cycles:

∆𝑇_𝑗𝑤 =_𝐼𝐶^{∆𝑉𝐶𝐸2 𝑁}

𝑤𝜌_𝑤𝑣_𝑤 =300×951×2869×0.004×2.5×0.004^{3129.7×𝑒4×10−5𝑁×𝑁} = 0.956 × 𝑒^{4×10−5𝑁}× 𝑁 (48)

∆𝑇_𝑗𝑠 =^∆𝑉_𝐼𝐶^{𝐺𝐸2𝑁}

𝑠𝜌_𝑠𝑣_𝑠 = ^3975.4×𝑒0.0026×10−5𝑁×𝑁

300×7370×150×0.00695∗0.00645×0.001= 267.37 × 𝑒^{0.0026×10−5𝑁}× 𝑁 (49) Therefore, the overall updated junction temperature is calculated using Equation (16) as shown in Figure 18.

Figure 18. Increasing pattern of junction temperature during power cycling.

Based on observation from Figure 18, the junction temperature increase reveals the impact of component degradation process on junction temperature as demonstrated by the slope of the curve increase over the number of cycles. Clear increase on the curve is observed as power cycling continues, which indicates the further component degradation process due to increase in the junction temperature.

With the overall junction temperature updated at each cycle, the expected component lifetime is calculated as:

𝑁_𝑓𝑠^′ = 0.5(^{𝐿∆𝐶𝑇𝐸∆𝑇}_𝛾𝑥 ^′)^1/𝑐 (50) 𝑁^′ = 𝐴∆𝑇^′𝛼𝑒𝑥𝑝 ( ^𝑄 ) (51)

The lifetime data for both components are assumed to follow normal distribution since normal distribution provides good fit to estimate the number of cycle to fail on component that under constant or random amplitude loading conditions [37]-[40]. It is testified by plotting fatigue life distributions in different probability papers and examining the goodness-of-fits of these distributions with chi-square techniques [46]. For the purpose of simplicity, a fix

proportion 30% of the expected life is considered for the variance for both components. Hence, the probabilistic model is updated with the increase junction temperature is given as:

𝑅′_𝑠(𝑁)~𝑛𝑜𝑟𝑚{𝜇′_𝑠(𝑁), 30%𝜇′_𝑠²(𝑁)} (52) 𝑅′_𝑤(𝑁)~𝑛𝑜𝑟𝑚{𝜇′_𝑤(𝑁), 30%𝜇′_𝑤²(𝑁)} (53) Based on Equations (39) and (40), the component reliability and system reliability are calculated at every specific cycle. For example, in pth cycle, if p is less than NSI, the system reliability is only dependent to the wire bond degradation process. Hence, the increase junction temperature due to it is calculated as:

𝑇_𝑗𝑤𝑝 = 0.956 × 𝑒^{4×10−5𝑁𝑝}× 𝑁_𝑝 (54) The overall junction temperature is computed as:

∆𝑇_𝑝′ = ∆𝑇_𝑗+ ∆𝑇_𝑗𝑤𝑝 = ∆𝑇 + 0.956 × 𝑒^{4×10−5𝑁𝑝}× 𝑁_𝑝 (55) With the updated component lifetime on wire bond computed with Equation (10) as:

𝑁_𝑓𝑤𝑝^′ = 𝐴∆𝑇_𝑝^′𝛼𝑒𝑥𝑝 (_𝑅𝑇^𝑄

𝑚) (56) the system reliability of IGBT module, according to Equation (13), is computed as:

𝑅_{𝑠𝑦𝑠𝑡𝑒𝑚} = 𝑅′_𝑤(𝑁 > 𝑁_𝑤^′) = 𝑛𝑜𝑟𝑚(𝑁_𝑝 > 𝑁_𝑓𝑤𝑝^′ ) (57) However, if p is greater than NSI, the system reliability is not only dependent to the wire bond degradation process, but also relies on the solder joint lifetime. Hence, the increase junction temperature due to both components is calculated respectively as:

𝑇_𝑗𝑤𝑝 = 0.956 × 𝑒^{4×10−5𝑁𝑝}× 𝑁_𝑝 (58)

∆𝑇_𝑗𝑠 = 267.37 × 𝑒^{0.0026×10−5𝑁𝑝} × 𝑁_𝑝 (59) The overall junction temperature is computed as:

∆𝑇_𝑝^′= ∆𝑇_𝑗+ ∆𝑇_𝑗𝑤𝑝+ ∆𝑇_𝑗𝑠

= ∆𝑇 + 0.956 × 𝑒^{4×10−5𝑁𝑝}× 𝑁_𝑝+ 267.37 × 𝑒^{0.0026×10−5𝑁𝑝}× 𝑁_𝑝 (60) With the updated component lifetime on wire bond and solder joint computed with

Equation (33) (34) as:

𝑁_𝑓𝑤𝑝^′ = 𝐴∆𝑇_𝑝^′𝛼𝑒𝑥𝑝 (_𝑅𝑇^𝑄

𝑚) (61) 𝑁_𝑓𝑠𝑝^′ = 0.5(^{𝐿∆𝐶𝑇𝐸∆𝑇}_𝛾𝑥 ^𝑝′)^1/𝑐 (62) the system reliability of IGBT module, according to Equation (38), is computed as:

𝑅_{𝑠𝑦𝑠𝑡𝑒𝑚}= 𝑅^′_𝑤(𝑁 > 𝑁_𝑤^′) × 𝑅^′_𝑠(𝑁 > 𝑁_𝑠^′)

= 𝑛𝑜𝑟𝑚(𝑁_𝑝 > 𝑁_𝑓𝑤𝑝^′ ) × 𝑛𝑜𝑟𝑚(𝑁_𝑠 > 𝑁_𝑓𝑠𝑝^′ ) (63) With this computing algorithm, the system reliability and the component reliability are computed at each cycle. The result is plotted in Figure 19. For the purpose of comparison, the system reliability with independent assumption, which does not consider failure mechanism interaction between crticial components, is also plotted in Figure 19.

Figure 19. Component reliability and system reliability.

In Figure 19, the system reliability with independent assumption and the system reliability are represented in the red curve and the green curve respectively. Meanwhile, the component reliability curves of wire bond and solder joint are marked in blue and brown accordingly. All curves have a decreasing pattern as the numbers of cycles continue. Early junction temperature increases is negligible and do not effect product lifetime since no sign of obvious fatigue is observed from Figure 19. As power cycling continues, the wire bond starts to fatigue as the blue curve declines after 150K cycles. Due to the increase junction temperature and the failure mechanism interaction, the solder joint degradation process follows at 200K cycles and both components’ degradation rates gradually rise especially after 250K cycles. The wire bond reliability curve is under the solder joint reliability curve during this power cycling test, meaning that the wire bond maintains its predominant failure mechanism and influences the system reliability the most since it fails faster. This confirms the observation of the

predominance of wire bond failure mechanism when temperature amplitude is under 130K in [34] [42] [44]. In such a case, reliability improvement on wire bonding area is critical and can result in late initiation of wire bond degradation process, which potentially alleviate the mutual

effect of failure interaction and postpones the solder joint degradation. Therefore, the system lifetime is enhanced and reliability is improved.

The system reliability with dependence and independence assumption are computed and plotted in Figure 19 as well. At the beginning of power cycling, the green curve and the red curve overlap with each other meaning there is no reliability prediction difference given only the wire bond degradation process is involved. However, as power cycling continues, huge

discrepancy emerges. This phenomenon is noted when the solder joint degradation process pitches in. From 190K cycles, at which solder joint starts to show recognizable drop on its reliability curves, the distinct gap between the red curve and the green curve is observed indicating the system is failing faster than it is predicted with the dependent assumption. With the consideration of failure interaction, the green curve clearly shows that system degrades faster than the red curve, meaning the proposed reliability method is able capture the interaction

between these two components’ failure mechanisms which the independent assumption fails to.

The effectiveness and accuracy of the proposed reliability method is amplified after 250K cycle, at which the system is functioning in its most vulnerable state and the mutual effect of

component failure mechanisms interaction is magnified due to the rapid increase in junction temperature. In Figure 18, junction temperature increases at faster rate after 250K cycles.

Meanwhile, in accordance, a sharp drop on system reliability after 250K cycles on the green curve can be observed in Figure 19. Based upon this phenomenon, the significant influences of the failure mechanism interaction and junction temperature on system reliability is demonstrated.

However, a smoother decreasing trend is shown on the red curve. Due to the assumption of independence relationship between components, the potential component failure mechanism interaction is not considered, which leads to invalid interpretation on system reliability especially

in the late stage of product life. Furthermore, the independence assumption computes the system reliability as the product of the component reliabilities as a series configuration, the computing result tends to emphasizes on the importance of the component that contributes a higher portion in the calculation. In our case, it is the wire bond due to its predominant failure mechanism.

Reflected in Figure 19, the red curve is almost parallel to the blue curve after 290K cycles. The reasoning above demonstrates the effectiveness and validity of the proposed reliability model and the rationale of considering failure interaction to provide more realistic estimates of system reliability. At the same time, reliability computation with the independence assumption might overestimate the system reliability and lead to errors.

.

5. CONCLUSION

In this work, a reliability prediction model is proposed to compute the system reliability of power electronic model capturing the failure mechanism interaction between critical

components: wire bond and solder joint. Wire bond and solder joint are important components for thermal, mechanical and electrical connection in IGBT module. The component degradation process is resulted from the stress strength caused by inhomogeneous component structure and temperature amplitude during power cycling. Additionally, failure interaction between

component failure modes affects component failure characteristics and is never precisely interpreted. However, most of the existing literatures fail to propose a comprehensive way to deal with IGBT system reliability with the consideration of failure interaction between

components. Therefore, the interest of this work is inspired and further proceeded to provide a realistic reliability assessment on PEM.

First, the degradation process of solder joint and wire bond is trigger due to the influence of thermo-mechanical stress. The failure characteristics of solder joint and wire bond are

captured via selected PoF model respectively. Dependent to the impact that the effect of thermal strains or temperature amplitude has on critical components many PoF models have been

established. To completely capture all the factors contributing to component degradation, component physical dimensions and material properties are taken account. Second, PoF models only estimate the average component lifetime. It does not provide any probabilistic interpretation for reliability assessment. Component lifetime often has variation and follows a certain

distribution, which is more of the case in reality. In order to provide realistic reliability analysis, the selected PoF models are converted into probabilistic models. Normal distribution is selected to describe the failure characteristics of component degradation process because fatigue data can

be approximated as normal distribution under random or constant loading condition [37]. Third, the failure interaction between wire bond and solder joint is studied. Wire bond lift-off is treated as the predominant failure mode based upon observed experiments [10] [32] and solder joint delamination is triggered by wire bond degradation process. Increased junction temperature is captured as it is affected by the degradation process of both components. Additionally, both wire bond and solder joint suffered increased thermo-mechanical stress as junction temperature rises.

Therefore, with updated junction temperature at each time, the expected component lifetime is estimated. In the end, the system reliability is computed in a series system configuration.

Dataset abstracted from [6] [34] and [42] are mainly used to study the failure characteristics of wire bond and solder joint for the contribution of the increase junction temperature. In addition, 3% change has been used as threshold criteria for initiation phase for solder joint. Nonlinear regression techniques via MINITAB have been used to develop the individual models for wire bond and solder joint respectively. Through Joule’s law, the increased junction temperature is computed based upon the regression models.

Reliability analysis was performed treating the system as a series configuration. System reliability is divided and computed into two phases. In the first phase, only the failure

mechanism of wire bond is take account due to its predominance and solder joint not showing any sign of fatigue. The system reliability is only dependent to the failure fatigue of wire bond.

The second phase begins when cracks initiated in solder joint. The system reliability is the product of reliability of solder joint and wire bond. Compared to the system reliability with independent assumption, the proposed model indicates earlier failure of the system. This demonstrates the necessity of capturing failure interaction and the acceleration of failure characteristics due the impact of failure interaction. From Figure 18, junction temperature

increases at a faster after 250K cycles. Accordingly, the system reliability has a faster drop after 250K cycles shown in Figure 19. This validates the choice of normal distribution for

probabilistic interpretation and the proposal model considering failure interaction between wire bond and solder joint.

In future research, the proposal model needs to be enhanced for various operating conditions incorporating various parameters. This allows more precise prediction on component lifetime for a wider range of applicable situations. Design of experiment can be under taken to find out the effective parameters if dataset is affluent. Comprehensive ANOVA approach can be adopted to accurately model the statistical behavior of VCE and VGE for regression model. Use of Bayesian model could be explored for a better insight into reliability behavior when fatigue data is available.

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